Mathematics practice questions

Practice and sample questions for Mathematics, organised by the topics of the exam programme. Every question has a ready-made explanation.

Topics and practice questions

Real numbers

Measurement. Elements of statistics. Sets. Elements of combinatorics and probability

Triangles

Coordinates. Transformations. Similarity. Vectors

Limits, continuity and derivatives. Applications of the derivative

Quadrilaterals and polygons

Functions and graphs

Exponential and logarithmic functions

Trigonometric functions. Trigonometric equations

Inequalities

Equations in one variable and word problems

Circle and disc

Polyhedra, their surface area and volume

Number sequences. Progressions

Areas of figures

Solids of revolution, their surface area and volume

Antiderivatives and integrals

nth roots. Irrational expressions. Powers with real exponents

Ratio. Proportion. Percentage

Systems of equations and word problems

Exponential and logarithmic equations, systems and inequalities

Points, lines and planes in space

Rational expressions

Complex numbers

Basic geometric figures

Sample questions

Each sample shows the correct answer and the explanation.

Question 1 · Real numbers

360 ədədinin natural bölənlərinin sayı neçədir?

Correct answer: C

Explanation

360 = 2³ · 3² · 5. Bölənlərin sayı üstlərin 1 artıqlarının hasilidir:(3 + 1)(2 + 1)(1 + 1) = 4 · 3 · 2 = 24.12 alınması 5 vuruğunun unudulması deməkdir. Düzgün cavab: C.

Question 2 · Limits, continuity and derivatives. Applications of the derivative

f(x) = x³ − 12x funksiyasının [−3; 3] parçasında ən böyük qiymətini tapın.

−9

Correct answer: B

Explanation

f'(x) = 3x² − 12 = 0 ⇒ x = ± 2. f(−3) = 9, f(−2) = −8 + 24 = 16, f(2) = −16, f(3) = −9. Ən böyük qiymət 16-dır. 9 cavabı yalnız parçanın uclarına baxmaqdan alınır. Düzgün cavab: B.

Question 3 · Measurement. Elements of statistics. Sets. Elements of combinatorics and probability

Qutuda 4 ağ və 6 qara top var. Topları geri qaytarmadan ardıcıl iki top çıxarırlar. İkisinin də ağ olması ehtimalı neçədir?

4/25

2/5

2/15

4/15

1/15

Correct answer: C

Explanation

Birinci top ağ olarsa, qutuda 9 top, onlardan 3-ü ağ qalır. Ehtimal 4/10 · 3/9 = 12/90 = 2/15. 4/25 = 4/10 · 4/10 hasili topun geri qaytarıldığı hala aiddir. Düzgün cavab: C.

Question 4 · Triangles

Düzbucaqlı üçbucağın katetləri 6 sm və 8 sm-dir. Hipotenuza çəkilmiş hündürlük neçə sm-dir?

2,4

3,6

4,8

Correct answer: E

Explanation

Hipotenuz 10 sm-dir. Üçbucağın sahəsini iki cür yazaq: 6 · 8 : 2 = 10 · h : 2, buradan h = 48 : 10 = 4,8 sm. 5 sm hipotenuza çəkilmiş medianın, 3,6 sm isə 6 sm-lik katetin proyeksiyasıdır. Düzgün cavab: E.

Question 5 · Coordinates. Transformations. Similarity. Vectors

M(2; 1) nöqtəsinə nəzərən mərkəzi simmetriyada C(−1; 4) nöqtəsinin obrazının koordinatları hansıdır?

(1; 5)

(3; −3)

(−5; 2)

(5; −2)

(−3; 3)

Correct answer: D

Explanation

M nöqtəsi CC' parçasının orta nöqtəsidir, ona görəC' = 2M − C = (4 + 1; 2 − 4) = (5; −2)(−5; 2) koordinat başlanğıcına nəzərən simmetriyadır, (3; −3) isə yalnız M − C vektorudur (ikiqat götürülməyib). Düzgün cavab: D.

Questions are in Azerbaijani, except in the English and Russian language subjects.

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Mathematics practice questions

Topics and practice questions

Sample questions

Start with your first question.

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